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At least 649 records · Page 36
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Aero-Optics of Hypersonic Turbulent Boundary Layers

Aero-optics refers to optical distortions due to index-of-refraction gradients that are induced by aerodynamic density gradients. At hypersonic flow conditions, the bulk velocity is many times the speed of sound and density gradients may originate from shock waves, compressible turbulent structures, acoustic waves, thermal variations, etc. Due to the combination of these factors, aero-optic distortions are expected to differ from those common to sub-sonic and lower super-sonic speeds. This report summarizes the results from a 2019-2022 Laboratory Directed Research and Development (LDRD) project led by Sandia National Laboratories in collaboration with the University of Notre Dame, New Mexico State University, and the Georgia Institute of Technology. Efforts extended experimental and simulation methodologies for the study of turbulent hypersonic boundary layers. Notable experimental advancements include development of spectral de-aliasing techniques for highspeed wavefront measurements, a Spatially Selective Wavefront Sensor (SSWFS) technique, new experimental data at Mach 8 and 14, a Quadrature Fringe Imaging Interferometer (QFII) technique for time-resolved index-of-refraction measures, and application of QFII to shock-heated air. At the same time, model advancements include aero-optic analysis of several Direct Numerical Simulation (DNS) datasets from Mach 0.5 to 14 and development of wall-modeled Large Eddy Simulation (LES) techniques for aero-optic predictions. At Mach 8 measured and predicted root mean square Optical Path Differences agree within confidence bounds but are higher than semi-empirical trends extrapolated from lower Mach conditions. Overall, results show that aero-optic effects in the hypersonic flow regime are not simple extensions from prior knowledge at lower speeds and instead reflect the added complexity of compressible hypersonic flow physics.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Constraint and size effects in confined layer plasticity

Plane strain finite element analyses are used to model the experiments for a thin metal layer confined between elastic solids. Here, the thin metal layer undergoes elastic-plastic deformations, here modelled by strain gradient plasticity, while the rest of the solid deforms only elastically. Plane strain is assumed and finite strains are accounted for. The microscopic boundary condition at the band interface is initially taken to be zero plastic strain increment, but plastic straining at the interface is allowed when the plastic strain gradient at the interface has exceeded a critical value. When the narrow metal band is inclined 45° relative to the direction of compression of the solid simple shear develops in the band and predictions are rather similar to those of a one-dimensional analysis for an infinite band. For a band at 90° the elastic parts give significant constraint on plastic flow, the stress fields are non-uniform along the band and the average nominal compressive stress shows strong sensitivity to the layer thickness and to the width of the specimen. Remarkably good qualitative, and in some cases quantitative, agreement is found with the experimental observations. Considering also other band angles, both the average nominal shear and compressive stress show variations with the angle.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A large deformation multiphase continuum mechanics model for shock loading of soft porous materials

A large deformation, coupled finite-element (FE) model is developed to simulate the multiphase response of soft porous materials subjected to high strain-rate loading. The approach is based on the theory of porous media (TPM) at large deformations. Simplifications to the one-dimensional regime studied in the numerical simulations follow. An overview of several different time integration schemes is presented for the purpose of solving the nonlinear dynamic coupled balance of momenta (mixture and fluid) and balance of mass of the mixture equations. Numerical examples are presented for (i) verification against closed-form analytical solutions assuming small loads, (ii) demonstrating large deformation effects at high strain-rate, and (iii) showing differences in deformations between a single-phase elastodynamics model with occluded compressible pore fluid and a multiphase poroelastodynamics model at high strain-rate. The multiphase model shows that the relative motion of the pore fluid significantly dampens the deformation response of the solid skeleton as compared to the single-phase model, and makes it possible to extract quantitative values for the stresses of the different constituents, thereby allowing one to form preliminary conclusions about the onset of damage in the solid skeleton. The novelty of the current work is developing a multiphase, large deformation, mixture theory numerical model for high strain-rate loading of soft porous materials. It was discovered that explicit, adaptive time-stepping Runge–Kutta schemes offer high accuracy at relatively low cost when compared to traditional implicit or explicit central difference time-stepping schemes for shock-like loadings. Here, shock viscosity is added to the mixture momentum balance equation to regularize the shock front, and a stabilization term is added to the mixture mass balance equation to stabilize equal order interpolation finite elements for the coupled finite element solution of multiphase materials.

Engineering↗
DOE OSTI2020

Dislocation-induced large local polarization inhomogeneity of ferroelectric materials

Dislocations in ferroelectrics play important roles in ferroelectricity, piezoelectricity, and dielectricity. However, the intrinsic charge-lattice coupling mechanism in ferroelectric crystals containing dislocations is still not well understood. Here, we report a large local polarization inhomogeneity of ~100 μCcm –2 induced by a single a[001] dislocation in the PbZr 0.2 Ti 0.8 O 3 /SrTiO 3 film/substrate heterostructure, the tensile region (~120 μCcm –2 ) and the compressive strain region (~21 μCcm –2 ) around the dislocation forms a butterfly-like area. Furthermore, this study reveals the dramatic effects of dislocations on local polarization and provides a strategy to manipulate the polarization magnitude and orientation of local polarization by defect engineering.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The effect of annealing on kink band formation in Ag/Fe nanolaminates

Kink banding is a common, though not well understood, failure mechanism in anisotropic materials such as nano metallic laminates (NMLs). In this work, we investigate the effect of annealing on kink band (KB) formation in Ag/Fe NMLs prepared by accumulative roll bonding (ARB) using in situ micropillar compression, scanning/transmission electron microscopy (S/TEM), and transmission Kikuchi diffraction (TKD) analyses. Our results show that annealing increases the KB initiation strain, decreases the probability of KB formation, and decreases the load drop magnitude accompanying kink banding in Ag/Fe NMLs. Post-compression analyses reveal that annealing facilitates more uniform deformation of pillars and affects the formation of geometrically necessary grain boundaries (GNBs) near the kink band boundary (KBB). Compared to its as-rolled counterpart, annealed Ag/Fe has wider KBs with blunter KBBs.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Suppressing Phase Segregation and Improving Stability in Mixed-Halide Perovskites through Spinel Oxide-Directed Epitaxy

Mixed-cation mixed-halide perovskite compositions are essential for achieving the required bandgaps for high-efficiency multijunction photovoltaics, yet their stability remains limited by interfacial defects, phase segregation, and degradation. Here, we introduce spinel oxides as a new family of lattice-matched substrates that enable crystalline, phase-pure, compositionally-uniform, bromide-rich perovskite film growth. The effect of spinel oxides is two-fold: reducing defects at the bottom interface by templating film growth and inducing beneficial compressive strain through mismatch-dependent substrate-perovskite lattice coupling. Spinel oxide substrates facilitate growth of highly crystalline films and eliminate detrimental secondary phases across thicknesses. Using grazing incidence X-ray diffraction, X-ray fluorescence, cathodoluminescence–scanning electron microscopy, cryogenic photoluminescence, and density functional theory, we reveal that Mg-halide bonds at the bottom interface induce lattice mismatch-dependent compressive strain that suppresses halide segregation and further reduces defect formation. In addition, films grown on spinel oxides maintain over 87% of the perovskite phase after 12 h under 100% relative humidity, as monitored by in situ grazing incidence wide-angle X-ray scattering (GIWAXS), compared to less than 70% for control samples. This work extends lattice matching from vapor-deposited epitaxial semiconductors to solution-processed halide perovskites to establish a broadly applicable strategy for defect suppression, phase homogenization, and long-term stability. Based on the fundamental science explored here, we set the stage for the development of lattice-matched spinel oxide charge transport layers to be integrated into perovskite solar cells and other optoelectronic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Directly driven magnetized fast-ignition targets with steep density gradients for inertial fusion energy

The development of advanced targets capable of achieving ignition with improved energy gain at lower driver energies is one of four key technical challenges to be solved in order to realize economical inertial fusion energy. We report the minimum energy necessary for a small hemispherical mass of fast-ignited high-density deuterium–tritium fuel to explosively ignite a significantly larger hemispherical mass of assembled cold fuel with much lower mass density, both with and without a flux-compressed magnetic field connecting the two regions. With the magnetic field, the burn rate improves, and lower energy states become more effective. The imploded fuel reservoir available in the lower-density, larger-mass region of the steep density gradient determines whether the fusion yield is several hundred MJ or up to a few GJ. We report a case wherein the cold reservoir ignited and produced high gain with the assistance of only ~700 kJ of hotspot yield, an amount that has already been demonstrated as feasible in laboratory experiments using indirect-drive targets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Thermal Radiation Transport with Tensor Trains

We present a novel tensor network algorithm to solve the time-dependent, gray thermal radiation transport equation. The method invokes a tensor train (TT) decomposition for the specific intensity. The efficiency of this approach is dictated by the rank of the decomposition. When the solution is “low rank,” the memory footprint of the specific intensity solution vector may be significantly compressed. The algorithm, following a step-then-truncate approach of a traditional discrete ordinates method, operates directly on the compressed state vector, thereby enabling large speedups for low-rank solutions. To achieve these speedups, we rely on a recently developed rounding approach based on the Gram-SVD. We detail how familiar S N algorithms for (gray) thermal transport can be mapped to this TT framework and present several numerical examples testing both the optically thick and thin regimes. The TT framework finds low-rank structure and supplies up to ≃60× speedups and ≃1000× compressions for problems demanding large angle counts, thereby enabling previously intractable SN calculations and supplying a promising avenue to mitigate ray effects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Hydrogen and Electric Charging Infrastructure for Heavy-Duty Trucks: A Nationally Scalable Megaregion Assessment

Decarbonizing regional and long-haul freight is challenging due to the limitations of battery-electric commercial vehicles and infrastructure constraints. Hydrogen fuel cell medium- and heavy-duty vehicles (MHDVs) offer a viable alternative, aligning with the decarbonization goals of the Department of Energy and commercial entities. Historically, alternative fuels like compressed natural gas and liquefied propane gas have faced slow adoption due to barriers like infrastructure availability. To avoid similar issues, effective planning and deploying zero-emission hydrogen fueling infrastructure is crucial. This research develops deployment plans for affordable, accessible, and sustainable hydrogen refueling stations, supporting stakeholders in the decarbonized commercial vehicle freight system. It aims to benefit underserved and rural energy-stressed communities by improving air quality, reducing noise pollution, and enhancing energy resiliency. This research also provides a blueprint for replacing diesel in over-the-road Class 8 freight truck applications with hydrogen fueling solutions. The study focuses on the Texas Triangle Megaregion (I-45, I-35, and I-10), the I-10 corridor between San Antonio, TX, and Los Angeles, CA, and the I-5/CA-99 corridors between Los Angeles, CA, and San Francisco, CA. This area represents a significant portion of U.S. heavy-duty freight movement, carrying ~8.5% of the national freight volume. Using the OR-AGENT (Optimal Regional Architecture Generation for Efficient National Transport) modeling framework, the study conducts an advanced assessment of commercial vehicles, road and freight networks, and energy systems. The framework integrates data on freight mobility, traffic, weather, and energy pathways to deliver a region-specific, optimized vehicles powertrain architectures, infrastructure deployment solutions, operational logistics, and energy pathways. By considering all vehicle origin-destination pairs utilizing these corridors and all feasible fueling station location options, the framework's genetic algorithm identifies the minimum number and optimal locations of hydrogen refueling stations, ensuring no vehicle is stranded. It also determines fuel schedules and quantities at each station. A roadmap for station deployment based on multiple adoption trajectories ensures a strategic rollout of hydrogen refueling infrastructure.

Sujan, Vivek [ORNL] (ORCID:0000000269882342)↗
DOE OSTI2020

Innovation in Radiological Security, Part 1 of 2 – Using a Cloud Solution to Compress the Timely Detection Model

The design and implementation of new security technologies must account for numerous and complex operational challenges. For example, traditionally isolated systems must now survive amid the proliferation of network connectivity and endure the dynamic environments created by organizations tolerating bring-your-own-device policies. When evaluating the cyber, physical, or cyber-physical security of an asset, a common practice in the security industry is to apply the Timely Detection Model (TDM)—a versatile concept that relates the security functions of detection, delay, and response to the progression of an oppositional force’s attack timeline. If implemented correctly, security enhancements can compress the TDM to offer efficiencies to the stakeholders responsible for adjudicating threat scenarios. The efficiencies gained by the response force allow for more effective protection strategies to be realized. One such enhancement, deployed within the radiological security domain—the Sentry-Remote Monitoring System (Sentry-RMS)—is a stand-alone security system that detects, assesses, and communicates priority alarms as a means of thwarting internal and external threats. The SEntry-RMS CommUnications and REsponse (Sentry-SECURE) platform—an optional feature of the Sentry-RMS—is being developed to facilitate more efficient alarm adjudication by site stakeholders and, if necessary, a faster response by law enforcement. This Cloud-hosted platform receives protected information from deployed Sentry-RMS units and relays it to stakeholders that have vested interests in maintaining an elevated level of situational awareness. Operationally, this enables real-time delivery of high-priority alarm and video imagery directly to an identified response stakeholder, such as local law enforcement or site management, via natively developed mobile applications or full platform integration. The Sentry-SECURE platform, as implemented by the U.S. Department of Energy’s Office of Radiological Security, is an example of an innovative security technology that compresses the TDM by (1) enabling a more efficient time to target and (2) better informing a response force’s predetermined tactics, techniques, and procedures. This paper explores the platform’s operational roles, highlights its principal functions, and presents a use case that demonstrates how the platform provides enhanced situational awareness when adjudicating priority alarms.

Sentry-RMS, Timely Detection Model, Sentry-SECURE↗
DOE OSTI2022

Sample Preparation and Experimental Design for In Situ Multi-Beam Transmission Electron Microscopy Irradiation Experiments

We discuss the need to understand materials exposed to overlapping extreme environments such as high temperature, radiation, or mechanical stress. When these stressors are combined there may be synergistic effects that enable unique microstructural evolution mechanisms to activate. Understanding of these mechanisms is necessary for the input and refinement of predictive models and critical for engineering of next generation materials. The basic physics and underlying mechanisms require advanced tools to be investigated. The in situ ion irradiation transmission electron microscope (I 3 TEM) is designed to explore these principles. To quantitatively probe the complex dynamic interactions in materials, careful preparation of samples and consideration of experimental design is required. Particular handling or preparation of samples can easily introduce damage or features that obfuscate the measurements. There is no one correct way to prepare a sample; however, many mistakes can be made. The most common errors and things to consider are highlighted within. The I 3 TEM has many adjustable variables and a large potential experimental space, therefore it is best to design experiments with a specific scientific question or questions in mind. Experiments have been performed on large number of sample geometries, material classes, and with many irradiation conditions. The following are a subset of examples that demonstrate unique in situ capabilities utilizing the I 3 TEM. Au nanoparticles prepared by drop casting have been used to investigate the effects of single ion strikes. Au thin films have been used in studies on the effects of multibeam irradiation on microstructure evolution. Zr films have been exposed to irradiation and mechanical tension to examine creep. Ag nanopillars were subjected to simultaneous high temperature, mechanical compression, and ion irradiation to study irradiation induced creep as well. These results impact fields including: structural materials, nuclear energy, energy storage, catalysis, and microelectronics in space environments.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Rheological Characterization of Biomass Feedstock for Alternative Energy Applications

With the increased necessity of alternative energy resources, bulk feedstock biomass materials were characterized with the purpose of replacing depleting energy supplies such as fossil fuels and other nonrenewable energy sources. Residual organic waste material (biomass) left over from agricultural processing and handling systems was recycled, and further investigated for renewable energy use. Understanding the scope of flowability for biomass material yielded more efficient, and economical crop harvesting, transporting, and storing method design for the agricultural industry. The effects of moisture on bulk solid flowability was investigated using a variety of parametric testing methods that measure basic flowability energy, and other properties such as compressibility and material resistance. In an industry where organic material is a wasteful byproduct, converting this biomass material into a new energy source and streamlining efficiently for innovative agricultural development supports a clean, renewable energy approach to everyday nonrenewable energy uses, such as oil, propane, and coal. As observed from the repeatable results from the investigated rheological material properties, biomass is an incredibly diverse material that requires modern engineering solutions to revolutionize biomass into a renewable energy source. Biomass will decarbonize petroleum (nonrenewable) derived fuels and chemicals, yielding recyclable carbon. This push to replace fossil fuels with recycled carbon is ideal because of the abundant, renewable, and otherwise agricultural waste of corn stover material. Decarburization, and reduction of C0 2 emissions reduces the effects of global warming.

09 BIOMASS FUELS↗
DOE OSTI2023

Effects of the surface termination and the oxygen vacancy position on LaNiO 3 ultra-thin films: First-principles study

In this study, while ultra-thin layers of the LaNiO 3 film exhibit a remarkable metal-insulator transition as the film thickness becomes smaller than a few unit cell (u.c.), the formation of possible oxygen vacancies and their effects on the correlated electronic structure have been rarely studied using first principles. Here, we investigate the effects of the surface termination and the oxygen vacancy position on the electronic properties and vacancy energetics of LaNiO 3 ultra-thin films under the compressive strain using density functional theory plus U (DFT + U). We find that oxygen vacancies can be easily formed in the Ni layers with the NiO 2 terminated surface (0.5 u.c. and 1.5 u.c. thickness) compared to the structures with the LaO terminated surface and the in-plane vacancy is energetically favored than the out-of-plane vacancy. When two vacancy sites are allowed, the Ni square plane geometry is energetically more stable in most cases as two oxygen vacancies tend to stay near a Ni ion. Strong anisotropy between the in-plane and out-of-plane vacancy formation as well as the layer and orbital dependent electronic structure occur due to strain, surface termination, charge reconstruction, and quantum confinement effects. The in-plane vacancy of the NiO 2 terminated structure is favored since the released charge due to the oxygen vacancy can be easily accommodated in the d x 2 -y 2 orbital, which is less occupied than the d z 2 orbital. Remarkably, the oxygen vacancy structure containing the Ni square-plane geometry becomes an insulating state in DFT + U with a sizable band gap of 1.2 eV because the large crystal field splitting between d z 2 and d x 2 -y 2 orbitals in the square-plane favors an insulating state and the Mott insulating state is induced in other Ni sites due to strong electronic correlations. In the thin-film structure without oxygen vacancies, the strong correlation effect in DFT + U drives a pseudogap ground state at the Fermi energy, similarly as the experimental photo-emission spectra; however, the variation of the DFT + U electronic structure depending on the surface termination becomes weaker compared to those obtained in DFT.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Velocity-space compression from Fermi acceleration with Lorentz scattering

The Fermi acceleration model describes how cosmic ray particles accelerate to great speeds by interacting with moving magnetic fields. In this work, we identify a variation of the model where light ions interact with a moving wall while undergoing pitch angle scattering through Coulomb collisions due to the presence of a heavier ionic species. The collisions introduce a stochastic component which adds complexity to the particle acceleration profile and sets it apart from collisionless Fermi acceleration models. The unusual effect captured by this simplified variation of Fermi acceleration is the nonconservation of phase space, with the possibility for a distribution of particles initially monotonically decreasing in energy to exhibit an energy peak upon compression. A peaked energy distribution might have interesting applications, such as to optimize fusion reactivity or to characterize astrophysical phenomena that exhibit nonthermal features.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Effect of rice husk ash-derived activator on the structural build-up of alkali activated materials

Highlights: • Filtered and unfiltered sodium silicate solutions were synthesised from RHA. • The dissolution efficiency of RHA in NaOH solution was 76.3%. • RHA-derived activator showed a structural build-up comparable to the commercial activator in AAM pastes. • The undissolved residues in the unfiltered RHA-derived activator increased the yield stress. • Comparable compressive strength and early age gel formation were observed from both commercial and RHA-derived solutions. Waste-derived sodium silicates (SSs) were synthesised from rice husk ash (RHA) to produce alkali activated materials (AAMs) using fly ash and slag as precursors. The effects of these SSs on the structural build-up were investigated by monitoring the evolution of the viscoelasticity, ultrasonic pulse waves, setting time, and infrared spectra. Two types of RHA derived SSs (filtered SS and unfiltered SS) were prepared to investigate the effect of the undissolved residue on the hardening process. The derived SS contained a large portion of monomer silicate species. The results showed that the structural build-up mechanism was comparable between the AAMs activated by the filtered SS and a commercial SS. The unfiltered SS increased the yield stress of the paste by up to 10 times. However, the residues in the unfiltered SS had insignificant impacts on the gel formation and compressive strength when using identical SiO{sub 2}/Na{sub 2}O and Na{sub 2}O/binder ratios in the mix design.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Real-fluid behavior in rapid compression machines: Does it matter?

Rapid compression machines (RCMs) have been extensively used to quantify fuel autoignition chemistry and validate chemical kinetic models at high-pressure conditions. Historically, the analyses of experimental and modeling RCM autoignition data have been conducted based on the adiabatic core hypothesis with ideal gas assumption, where real-fluid behavior has been completely overlooked, though this might be significant at common RCM test conditions. Here, this work presents a first-of-its-kind study that addresses two significant but overlooked questions for autoignition studies within RCMs in the fundamental combustion community: (i) experiment-wise, can unaccounted-for real-fluid behavior in RCMs affect the interpretation and analysis of RCM experimental data? and (ii) simulation-wise, can unaccounted-for real-fluid behavior in RCMs affect RCM autoignition modeling and the validation of chemical kinetic models? To this end, theories for real-fluid isentropic change are newly proposed and derived based on high-order Virial EoS, and are further incorporated into an effective-volume real-fluid autoignition modeling framework newly developed for RCMs. With detailed analyses, the strong real-fluid behavior in representative RCM tests is confirmed, which can greatly influence the interpretation of RCM autoignition experiments, particularly the determination of end-of-compression temperature and evolution of the adiabatic core in the reaction chamber. Furthermore, real-fluid RCM modeling results reveal that considerable error can be introduced into simulating RCM autoignition experiments when following the community-wide accepted effective-volume approach by assuming ideal-gas behavior, which can be as high as 64% in the simulated ignition delay time at compressed pressure of 125 bar and lead to contradictory validation results of chemical kinetic models. Therefore, we recommend the community to adopt frameworks with real-fluid behavior fully accounted for (e.g., the one developed in this study) to analyze and simulate past and future RCM experiments, so as to avoid misinterpretation of RCM autoignition experiments and eliminate the potential errors that can be introduced into the simulation results with the existing RCM modeling frameworks.

High-order Virial equation of state↗
DOE OSTI2022

Optimization of screw design for continuous wet granulation: A case study of metoprolol succinate ER tablets

This study aimed at understanding the effect of screw design on the critical characteristics of granules and tablets of an extended-release (ER) formulation for twin screw granulation process. The screw design parameters assessed included number of kneading elements (KEs) per kneading zone, distance separating kneading zones, staggering angle (SA) of kneading elements and number of sizing elements (SEs). These input variables were varied using a design of experiment (DoE) approach to manufacture granules. Particle size distribution (PSD), flow and bulk properties of the granules, breaking strength and dissolution of tablets manufactured using these granules were characterized. The results of least square fitting showed that KEs, SA, and SEs of the screws significantly (p -values < 0.05) affected the PSD, cohesion, compressibility (CPS), conditioned bulk density (CBD) and permeability of the granules. The KEs and SEs significantly (p -value < 0.05) affected the dissolution, which was attributed to their effects on CPS and CBD of the granules. The distance between kneading zones had no significant effect on granules and tablet characteristics. Finally, these results may be used to further study the interaction of the identified critical screw design parameters with other processing parameters for continuous manufacturing of this ER matrix-based tablet formulation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

A Tensor Network-Based Quantum Algorithm for the Nonlinear 1D Burgers' Equation

In this work, we implement a tensor network-based quantum algorithm to solve unsteady, nonlinear partial differential equations (PDEs). The challenge lies in how to effectively represent, encode, process, and evolve the nonlinear system of PDEs on quantum computers. We will discuss the new techniques using the compressible 1-dimensional (1D) Burgers' equation as an example, because it represents the fundamental nonlinear feature and yet removes certain complexity in physics, allowing us to focus on the design of quantum algorithms. Previous attempts to solve nonlinear PDEs in quantum computation have often involved storing multiple copies of solutions or employing linearizations. Neither is practical due to exponential scaling with evolution time or insufficient solution accuracy. Our framework is based on matrix product states (MPSs) and matrix product operators (MPOs). For example, the velocity field is represented by MPS, whereas the linear and nonlinear spatial differential terms of the velocity field are processed by MPOs. Our primary focus herein is to verify and validate the various tensor network components of the algorithm using solutions obtained by the classical algorithms on high performance computing (HPC) architectures. We use a classical time marching method to demonstrate the functionality of the tensor network operations to model the PDE and their robustness with the time evolution of the system. Our classical simulation results demonstrate the utility of tensor network-based operations in modeling nonlinear PDEs and highlight the necessity as well as potential advantages of using quantum simulations for these techniques.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗